Contribution and Reservation

(11·10¹⁹⁶+61)/9 =: 1(2)₁₉₅9_<197>; = 7 · 743 · [2349975432075028306522249994659146745284026576085795466683757397081757781623192121173278642996005041765472451878912175009079450533017154820654147706637612424961011771240573394005426306906791429_<193>] SUBMIT/RESERVE

Status

Expression:	(11·10¹⁹⁶+61)/9
Composite Factor:	234997543207502830652224999465914674528402657608579546668375 739708175778162319212117327864299600504176547245187891217500 907945053301715482065414770663761242496101177124057339400542 6306906791429 (193-digit)
Status:	Not factored. Not reserved. You can submit its factors or reserve it for submitting in the future.

How to factor it

ECM, P-1, P+1

Look for prime factors by GMP-ECM first. Refer to the section "Efforts by ECM". Not only ECM but also P-1/P+1 may be helpful.

NFS

Use GGNFS and/or Msieve if GMP-ECM cannot find a factor. The SNFS difficulty of this composite number is 197.04-digit and the GNFS difficulty is 192.37-digit. SNFS must be faster than GNFS. It will take about 15 CPU-days to factor this composite number on 64-bit Opteron-2600MHz.

Steps of SNFS

Put factMsieve.pl to which $GGNFS_BIN_PATH and $NUM_CPUS were modified properly in the working directory 12229_196.
Put the following polynomial file 12229_196.poly in there too.
And then, run "perl factMsieve.pl 12229_196".

12229_196.poly

n: 2349975432075028306522249994659146745284026576085795466683757397081757781623192121173278642996005041765472451878912175009079450533017154820654147706637612424961011771240573394005426306906791429
m: 1000000000000000000000000000000000000000
deg: 5
c5: 110
c0: 61
skew: 0.89
type: snfs
lss: 1
rlim: 13500000
alim: 13500000
lpbr: 28
lpba: 28
mfbr: 55
mfba: 55
rlambda: 2.5
alambda: 2.5

These parameters were not fully adjusted. The approximate expressions which were used for making the parameters are: deg=expt<=105?4:expt<=210?5:6 or expt<=144?4:6; d=log10(c[deg])+deg*log10(m)[digits]; time=10^(d/30-4)[hours]; skew=|c0/c[deg]|^(1/deg); rlim=round(7*10^(d/60+3)); lpbr=floor(d/25+21); mfbr=floor(d/8+31); rlambda=floor(d/25+18)/10;

Efforts by ECM

The efforts by ECM to find small factors of this 193-digit composite number so far are as follows. According to the reports, unknown prime factors of this composite number are probably 45-digit or more. Please report your efforts by ECM. (Anonymous reports are not acceptable)

Level	B1	Reported runs Total / Required runs (Required runs for lower level)	Name
45	11e6	0 / 0
50	43e6	1130	yoyo@home	Jan 15, 2010
		1130 / 7465
		/ 6335
55	11e7	0 / 17348 (2628)
55	11e7	/ 17348 (2628)
60	26e7	0 / 41882 (7462)
60	26e7	/ 41882 (7462)
65	85e7	0 / 69380 (13568)
65	85e7	/ 69380 (13568)

Command line to find prime factors up to about 50-digit

echo 2349975432075028306522249994659146745284026576085795466683757397081757781623192121173278642996005041765472451878912175009079450533017154820654147706637612424961011771240573394005426306906791429 | ecm -n -c 6335 43e6

Command line to find prime factors up to about 55-digit

echo 2349975432075028306522249994659146745284026576085795466683757397081757781623192121173278642996005041765472451878912175009079450533017154820654147706637612424961011771240573394005426306906791429 | ecm -n -c 17348 11e7

Command line to find prime factors up to about 60-digit

echo 2349975432075028306522249994659146745284026576085795466683757397081757781623192121173278642996005041765472451878912175009079450533017154820654147706637612424961011771240573394005426306906791429 | ecm -n -c 41882 26e7

Command line to find prime factors up to about 65-digit

echo 2349975432075028306522249994659146745284026576085795466683757397081757781623192121173278642996005041765472451878912175009079450533017154820654147706637612424961011771240573394005426306906791429 | ecm -n -c 69380 85e7

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